Problem: If \(log{}_{2}x=7\),find \(log{}_{8}x.\)

**I am not allowed to use a calculator on this problem. **

These are steps I have so far:

2^{7}=x

x=128

log_{8}128=y

8^{y}=128

y=\(\frac{log 128}{log 8}\)

And this is where I am stuck. I have to use a calculator for this part. Is there a way to solve this without using a calculator?

Thanks.

LightningSidd Jun 19, 2021

#1**+3 **

So far, you're doing really well..

After \(y = {log128\over log8}\) you don't really need a calculator to solve this

We can write this as

\(y= {log 2^7\over log 2^3}\) right?

then \(y= {7log2\over 3log2}\)

⇒\(y={7\over 3}\)

\({log}_{8}x = {7\over 3}\)

Hope you got it :)

amygdaleon305 Jun 19, 2021

#2**+2 **

Oh yea you can write it like that then use the log rules and division. Thanks for the help!

LightningSidd
Jun 19, 2021